1,720,990 research outputs found
Huygens' principle and a Paley-Wiener type Theorem on Damek-Ricci spaces
No full textWe prove that Huygens' principle and the principle of equipartition of energy hold
for the modified wave equation on odd dimensional Damek-Ricci spaces. We also
prove a Paley-Wiener type theorem for the inverse of the Helgason Fourier transform on
Damek-Ricci spaces
The Gelfand transform of homogeneous distributions of Heisenberg type groups
No full textA distribution on a Heisenberg type group of homogeneous dimension Q is a biradial kernel of type a if
it coincides with a biradial function, homogeneous of degree a −Q, and smooth away from the identity.
We prove that a distribution is a biradial kernel of type a, 0
≤a<Q, if and only if its Gelfand transform,
defined on the Heisenberg fan, extends to a smooth even function on the upper half plane, homogeneous
of degree −a/2. A similar result holds for radial kernels on the Heisenberg group
Sobolev spaces and the Cayley transform
No full textThe generalised Cayley transform C
from an Iwasawa N-group
into the corresponding real unit sphere S
induces
isomorphisms between suitable Sobolev spaces
H^\alpha(S) and H^\alpha(N).
We study the differential of C
and we obtain a criterion for a function
to be in H^\alpha(S)
Some properties of horocycles on Damek-Ricci spaces
No full textWe prove that a Damek–Ricci space is symmetric if and only if the geodesic inversion
preserves the set of horocycles
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